Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 213, 754, 68 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 213, 754, 68 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 213, 754, 68 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 213, 754, 68 is 1.
HCF(213, 754, 68) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 213, 754, 68 is 1.
Step 1: Since 754 > 213, we apply the division lemma to 754 and 213, to get
754 = 213 x 3 + 115
Step 2: Since the reminder 213 ≠ 0, we apply division lemma to 115 and 213, to get
213 = 115 x 1 + 98
Step 3: We consider the new divisor 115 and the new remainder 98, and apply the division lemma to get
115 = 98 x 1 + 17
We consider the new divisor 98 and the new remainder 17,and apply the division lemma to get
98 = 17 x 5 + 13
We consider the new divisor 17 and the new remainder 13,and apply the division lemma to get
17 = 13 x 1 + 4
We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get
13 = 4 x 3 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 213 and 754 is 1
Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(17,13) = HCF(98,17) = HCF(115,98) = HCF(213,115) = HCF(754,213) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 68 > 1, we apply the division lemma to 68 and 1, to get
68 = 1 x 68 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 68 is 1
Notice that 1 = HCF(68,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 213, 754, 68?
Answer: HCF of 213, 754, 68 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 213, 754, 68 using Euclid's Algorithm?
Answer: For arbitrary numbers 213, 754, 68 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.